The document proposes a new metaheuristic optimization algorithm called the Bat Algorithm (BA) which is inspired by the echolocation behavior of microbats. The BA idealizes how bats use echolocation to locate prey and avoid obstacles. It formulates rules to govern how virtual "bats" change their pulse frequencies, loudness, and locations to search for the optimal solution. Simulations show the BA performs well on benchmark test functions, finding the global minimum solutions. The author believes combining advantages of existing algorithms led to developing this new BA which seems superior and warrants further study.
This document proposes a new metaheuristic optimization algorithm called the Bat Algorithm, which is inspired by the echolocation behavior of microbats. It first describes how real microbats use echolocation to detect prey and navigate, then outlines how the key aspects of echolocation are abstracted and modeled mathematically to formulate new optimization rules. The algorithm is compared to other nature-inspired algorithms like genetic algorithms and particle swarm optimization, showing promising results.
Bat Algorithm: Literature Review and ApplicationsXin-She Yang
This document provides a literature review of the Bat Algorithm, which is a bio-inspired metaheuristic optimization algorithm based on the echolocation behavior of bats. The summary reviews the key aspects of the standard Bat Algorithm, including how it models the pulse rates and loudness of bats to balance exploration and exploitation. Variants of the Bat Algorithm are also discussed. Applications of the Bat Algorithm and its variants to diverse optimization problems are reviewed. Further research topics on improving the algorithm are proposed.
Bat algorithm is metaheuristic that can be applied for global optimization. It was inspired by the echolocation behaviour of microbats, with varying pulse rates of emission and loudness
1. A spectrophotometer works by separating light into wavelengths using a diffraction grating and measuring how much light is absorbed by a sample. Some light is absorbed when the electrons in sample molecules absorb specific wavelengths of energy and become excited.
2. Absorption follows Beer's law, where absorbance is directly proportional to concentration and path length. Transmittance is measured to calculate absorbance.
3. Graphs of absorbance versus concentration or path length will produce straight lines, demonstrating the direct proportionality as described by Beer's law.
TSSB Brain Initiative - Overview of Nano and Molecular Communications and Bra...Walton Institute
This was a presentation given by Dr. Sasitharan Balasubramaniam, Director of Research at TSSG, in which he presented his current research in developing miniature devices for Brain implants. The talk focused on two types of implants, which includes (i) nanoelectronics that are used to stimulate neutrons, (ii) engineered cells that transfect and communicate to neurons. The talk will also touch on the potential applications for these types of devices.
This document provides an overview of UV/Visible spectroscopy. It begins with definitions of spectroscopy and discusses the principles, including that spectroscopy involves measuring the absorption or emission of electromagnetic radiation by molecules as they change energy states. It also defines key terms like chromophores, auxochromes, and discusses different types of electronic transitions that can occur. The document then discusses instrumentation components like sources of radiation, collimating systems, monochromators, and detectors. It provides details on various types of sources, monochromators, and filters. In summary, the document provides a comprehensive introduction to the theory, applications, and instrumentation of UV/Visible spectroscopy.
UV-VIS spectroscopy analyzes the absorption of light in the ultraviolet-visible spectral region by molecules. White light is composed of a range of wavelengths, which can be separated by a prism into the visible colors from violet to red. Different functional groups and conjugated systems in molecules absorb at characteristic wavelengths. The absorbance of a solution is proportional to the concentration of the absorbing species, as described by Beer's Law. UV-VIS spectroscopy is used to determine structural features and study reactions.
OBT751 Analytical methods Instrumentation materialsMercy Joseph
Instrumental methods of analysis have several advantages over chemical methods, including requiring only small sample sizes, being faster, and being able to analyze complex mixtures. The basic functions of instrumental analysis are signal generation, transduction, amplification, and presentation. Instrumental techniques are divided into spectroscopy, electrochemistry, and chromatography. Noise in instrumental analysis can come from chemical, instrumental, thermal, shot, flicker, or environmental sources. Hardware techniques can help reduce environmental, flicker, and transducer noise through methods like filters, choppers, shields, modulators, and synchronous detection.
This document proposes a new metaheuristic optimization algorithm called the Bat Algorithm, which is inspired by the echolocation behavior of microbats. It first describes how real microbats use echolocation to detect prey and navigate, then outlines how the key aspects of echolocation are abstracted and modeled mathematically to formulate new optimization rules. The algorithm is compared to other nature-inspired algorithms like genetic algorithms and particle swarm optimization, showing promising results.
Bat Algorithm: Literature Review and ApplicationsXin-She Yang
This document provides a literature review of the Bat Algorithm, which is a bio-inspired metaheuristic optimization algorithm based on the echolocation behavior of bats. The summary reviews the key aspects of the standard Bat Algorithm, including how it models the pulse rates and loudness of bats to balance exploration and exploitation. Variants of the Bat Algorithm are also discussed. Applications of the Bat Algorithm and its variants to diverse optimization problems are reviewed. Further research topics on improving the algorithm are proposed.
Bat algorithm is metaheuristic that can be applied for global optimization. It was inspired by the echolocation behaviour of microbats, with varying pulse rates of emission and loudness
1. A spectrophotometer works by separating light into wavelengths using a diffraction grating and measuring how much light is absorbed by a sample. Some light is absorbed when the electrons in sample molecules absorb specific wavelengths of energy and become excited.
2. Absorption follows Beer's law, where absorbance is directly proportional to concentration and path length. Transmittance is measured to calculate absorbance.
3. Graphs of absorbance versus concentration or path length will produce straight lines, demonstrating the direct proportionality as described by Beer's law.
TSSB Brain Initiative - Overview of Nano and Molecular Communications and Bra...Walton Institute
This was a presentation given by Dr. Sasitharan Balasubramaniam, Director of Research at TSSG, in which he presented his current research in developing miniature devices for Brain implants. The talk focused on two types of implants, which includes (i) nanoelectronics that are used to stimulate neutrons, (ii) engineered cells that transfect and communicate to neurons. The talk will also touch on the potential applications for these types of devices.
This document provides an overview of UV/Visible spectroscopy. It begins with definitions of spectroscopy and discusses the principles, including that spectroscopy involves measuring the absorption or emission of electromagnetic radiation by molecules as they change energy states. It also defines key terms like chromophores, auxochromes, and discusses different types of electronic transitions that can occur. The document then discusses instrumentation components like sources of radiation, collimating systems, monochromators, and detectors. It provides details on various types of sources, monochromators, and filters. In summary, the document provides a comprehensive introduction to the theory, applications, and instrumentation of UV/Visible spectroscopy.
UV-VIS spectroscopy analyzes the absorption of light in the ultraviolet-visible spectral region by molecules. White light is composed of a range of wavelengths, which can be separated by a prism into the visible colors from violet to red. Different functional groups and conjugated systems in molecules absorb at characteristic wavelengths. The absorbance of a solution is proportional to the concentration of the absorbing species, as described by Beer's Law. UV-VIS spectroscopy is used to determine structural features and study reactions.
OBT751 Analytical methods Instrumentation materialsMercy Joseph
Instrumental methods of analysis have several advantages over chemical methods, including requiring only small sample sizes, being faster, and being able to analyze complex mixtures. The basic functions of instrumental analysis are signal generation, transduction, amplification, and presentation. Instrumental techniques are divided into spectroscopy, electrochemistry, and chromatography. Noise in instrumental analysis can come from chemical, instrumental, thermal, shot, flicker, or environmental sources. Hardware techniques can help reduce environmental, flicker, and transducer noise through methods like filters, choppers, shields, modulators, and synchronous detection.
Principle and instrumentation of UV-visible spectrophotometer.Protik Biswas
UV-visible spectrophotometry uses light in the ultraviolet and visible range to analyze substances. When light passes through a sample, some is absorbed and some is transmitted. The ratio of light entering versus exiting the sample is used to calculate absorbance, which follows Beer's Law - absorbance is directly proportional to concentration. A spectrophotometer consists of a light source, monochromator to isolate wavelengths, sample holder, and detector to measure transmitted light intensity and thus absorbance. This allows analysis of concentration for substances that absorb specific wavelengths of UV or visible light.
Spectroscopy is the measurement and interpretation of electromagnetic radiation absorbed or emitted when the molecules or atoms or ions of a sample move from one energy state to another energy state. UV spectroscopy is a type of absorption spectroscopy in which light of the ultra-violet region (200-400 nm) is absorbed by the molecule which results in the excitation of the electrons from the ground state to a higher energy state.Basically, spectroscopy is related to the interaction of light with matter.
As light is absorbed by matter, the result is an increase in the energy content of the atoms or molecules.
When ultraviolet radiations are absorbed, this results in the excitation of the electrons from the ground state towards a higher energy state.
Molecules containing π-electrons or nonbonding electrons (n-electrons) can absorb energy in the form of ultraviolet light to excite these electrons to higher anti-bonding molecular orbitals.
The more easily excited the electrons, the longer the wavelength of light they can absorb. There are four possible types of transitions (π–π*, n–π*, σ–σ*, and n–σ*), and they can be ordered as follows: σ–σ* > n–σ* > π–π* > n–π* The absorption of ultraviolet light by a chemical compound will produce a distinct spectrum that aids in the identification of the compound.
This document summarizes key concepts from a chapter on atomic structure:
1. Electromagnetic radiation consists of oscillating electric and magnetic fields that propagate as waves. Light is a type of electromagnetic radiation detectable by the human eye.
2. Atoms can only absorb or emit electromagnetic radiation at specific quantized energy levels. This explains the emission spectrum of hydrogen, which shows only certain discrete wavelengths.
3. Niels Bohr's early model of the hydrogen atom proposed that electrons orbit the nucleus at fixed distances corresponding to discrete energy levels. Later, the quantum mechanical model described electron behavior as wave-like standing waves.
4. Werner Heisenberg's uncertainty principle states that the more precisely the position
UV-visible spectroscopy is a technique that uses light in the visible and adjacent ranges. It works by measuring how much light is absorbed by a sample at each wavelength.
The document discusses the basic principles of spectroscopy, including how electromagnetic radiation interacts with matter. It describes the laws of absorption, specifically Beer's law, which states that absorbance is proportional to concentration.
The key aspects of instrumentation are outlined, including light sources, wavelength selectors like monochromators, sample holders, and detection devices. Single beam and double beam spectrophotometers are explained as the main types of instruments used in UV-visible spectroscopy.
The document summarizes a presentation given by Sulabh Pal, Suresh Kumar, and Himanshu Srivastava on April 27th 2012 about an ant colony optimization technique proposed for edge detection in images. The presentation covered the historical background of ant colony optimization, described how it works by modeling the behavior of ant colonies, and presented experimental results showing that the proposed approach improves edge detection compared to traditional methods and has shorter computation time than traditional ant colony optimization. The technique was also discussed as having applications in optimization problems like routing in communication networks.
- The document is a presentation on ultraviolet spectroscopy submitted by Moriyom Akhter and Md Shah Alam from the Department of Pharmacy at World University of Bangladesh.
- It defines ultraviolet spectroscopy and discusses key concepts like absorption spectra, types of electronic transitions that can occur, Beer's and Lambert's absorption laws, instrumentation components, and applications in qualitative and quantitative analysis.
- The presentation also examines effects of chromophores and auxochromes on absorption spectra and maximum wavelengths, and how solvents can shift absorption peaks.
Spectroscopy involves the interaction of electromagnetic radiation with matter. Spectroscopic methods are used to elucidate molecular structure and quantify inorganic and organic compounds. There are several regions of the electromagnetic spectrum used including X-ray, UV, visible, and IR. Important concepts include Beer's law, which states absorbance is proportional to concentration, molar absorptivity, and path length. Spectrophotometry is used for qualitative and quantitative analysis in areas such as determining unknown concentrations. Fluorescence also provides a sensitive technique where molecules emit light at longer wavelengths after absorbing radiation.
This document discusses the Beer-Lambert law, which states that the absorbance of light as it passes through a substance is directly proportional to the concentration of that substance and the path length. It provides the mathematical expression of the Beer-Lambert law and defines terms such as transmittance and absorbance. The document explains that absorbance is preferred over transmittance for expressing the Beer-Lambert law because absorbance results in a linear relationship with concentration that allows for simple quantitative analysis. Several examples are provided to demonstrate applications of the Beer-Lambert law.
This document provides an introduction to spectrometric methods and the Beer-Lambert law. It defines key terms like absorbance, transmittance, molar absorptivity, and wavelength. The Beer-Lambert law states that absorbance is directly proportional to concentration, path length, and molar absorptivity. It also explains that absorbance follows a linear relationship with concentration at a given path length and wavelength for a single analyte. Deviations from Beer's law can occur under certain circumstances.
This document provides an overview of UV-Visible spectroscopy. It discusses how UV radiation causes electronic transitions in molecules, which can be observed via absorption spectroscopy. The instrumentation used includes sources of UV and visible light, a monochromator to select wavelengths, and a detector. Samples are dissolved and placed in transparent cuvettes for analysis. Spectra are recorded as absorbances and show absorption bands corresponding to electronic transitions. UV-Vis is useful for structure elucidation and quantitative analysis.
UV-Visible spectroscopy involves absorption of ultraviolet or visible light by molecules. This absorption causes electrons to move to higher energy molecular orbitals. The Beer-Lambert law states that absorbance is directly proportional to concentration and path length. Deviations from Beer-Lambert law can occur at high concentrations due to interactions between molecules, or if non-monochromatic light is used. UV-Visible spectroscopy is used to study electronic transitions and structure of molecules.
Solving Quadratic Assignment Problems (QAP) using Ant Colony SystemAjay Bidyarthy
The document describes using an ant colony system algorithm to solve quadratic assignment problems (QAP). QAPs have applications in operations research, parallel computing, and combinatorial data analysis. The ant colony system is applied to QAP by modeling it as assigning activities to locations. Ants probabilistically construct solutions based on pheromone trails and distance/flow matrices. The algorithm runs in O(mn2k) time which is faster than exact solutions for large problems. Example problems and results demonstrating the ant colony system finding near-optimal solutions to standard QAP test cases are presented.
UV spectroscopy can be used to analyze organic compounds. It works by measuring the absorption of UV or visible light. Double beam UV spectroscopy has advantages over single beam as it automatically corrects for fluctuations in light source intensity and detector response. UV spectroscopy can be used to detect impurities, characterize functional groups, and determine concentrations through the Beer-Lambert law. It provides structural information about organic compounds.
UV-VIS spectroscopy involves using ultraviolet or visible light to illuminate a sample and analyzing the light that is absorbed. Electronic transitions in molecules can be detected by observing which wavelengths of light are absorbed. This provides information about functional groups and conjugated systems present in the sample. A UV-VIS spectrophotometer directs light from a source through the sample solution and a monochromator selects wavelengths, which are then measured by a detector. The amount of light absorbed at each wavelength follows Beer's Law, allowing for determination of concentrations from a calibration curve.
The document discusses the derivation of Beer-Lambert's law, which relates the absorption of light to the properties of the material through which the light is passing. Lambert first derived a relationship showing that the decrease in light intensity through a medium is directly proportional to the intensity and thickness of the medium. Beer later extended this by showing absorption also depends on the concentration of the absorbing solution. Together, Beer and Lambert derived an equation, now known as Beer-Lambert's law, that quantifies the relationship between light absorption and intensity, thickness of the medium, and concentration of an absorbing solution. The law has limitations in that it applies only to monochromatic, unscattered light passing through dilute solutions.
The document discusses UV-Vis spectroscopy, including an introduction to electronic transitions observed in UV-Vis spectroscopy, instrumentation used in UV-Vis spectroscopy, and components of UV-Vis spectrometers such as sources, sample containers, monochromators, and detectors. Selection rules that determine which electronic transitions are allowed are also covered.
UV-Vis spectroscopy involves using spectroscopy to study the interaction between electromagnetic radiation and matter. It summarizes that UV-Vis spectroscopy uses electromagnetic waves in the UV and visible spectral regions to analyze molecules and their electronic transitions. The document discusses the wave and particle theories of light, the electromagnetic spectrum, Beer-Lambert law which relates absorbance to concentration, and limitations of the Beer-Lambert law such as deviations at high/low concentrations and due to fluorescence or turbidity.
Bat Algorithm is Better Than Intermittent Search StrategyXin-She Yang
This document compares the bat algorithm to the intermittent search strategy for balancing exploration and exploitation in metaheuristic optimization algorithms. It reviews several metaheuristic algorithms and analyzes the theoretical basis for optimal balancing of exploration and exploitation phases. Equations are presented for the optimal ratio of exploration and exploitation phases in 2D problems based on the intermittent search strategy. The bat algorithm is described and its ability to achieve near-optimal balancing is demonstrated through numerical experiments on test functions. The document concludes higher dimensional problems require more exploration effort to find global optima with limited computations.
This document summarizes a research paper that proposes a new swarm intelligence algorithm called a Hybrid Bat Algorithm. The Hybrid Bat Algorithm combines the original Bat Algorithm with strategies from Differential Evolution. The Bat Algorithm is based on the echolocation behavior of bats and has been shown to effectively solve lower-dimensional optimization problems. However, it can struggle with higher-dimensional problems due to its tendency to converge quickly. The researchers propose hybridizing it with Differential Evolution strategies to improve its performance on higher-dimensional problems. They test the Hybrid Bat Algorithm on standard benchmark functions and find that it significantly outperforms the original Bat Algorithm.
A New Metaheuristic Bat-Inspired AlgorithmXin-She Yang
This document proposes a new metaheuristic optimization algorithm called the Bat Algorithm (BA) which is inspired by the echolocation behavior of microbats. Microbats use echolocation to detect prey and navigate in darkness by emitting ultrasonic pulses and analyzing the echo. The BA idealizes these behaviors to develop rules for how "bats" can search for the optimal solution. Key behaviors include adjusting pulse rates and loudness based on proximity to the target solution. The BA shows potential to combine advantages of other algorithms like PSO and is shown to perform well in simulations.
Principle and instrumentation of UV-visible spectrophotometer.Protik Biswas
UV-visible spectrophotometry uses light in the ultraviolet and visible range to analyze substances. When light passes through a sample, some is absorbed and some is transmitted. The ratio of light entering versus exiting the sample is used to calculate absorbance, which follows Beer's Law - absorbance is directly proportional to concentration. A spectrophotometer consists of a light source, monochromator to isolate wavelengths, sample holder, and detector to measure transmitted light intensity and thus absorbance. This allows analysis of concentration for substances that absorb specific wavelengths of UV or visible light.
Spectroscopy is the measurement and interpretation of electromagnetic radiation absorbed or emitted when the molecules or atoms or ions of a sample move from one energy state to another energy state. UV spectroscopy is a type of absorption spectroscopy in which light of the ultra-violet region (200-400 nm) is absorbed by the molecule which results in the excitation of the electrons from the ground state to a higher energy state.Basically, spectroscopy is related to the interaction of light with matter.
As light is absorbed by matter, the result is an increase in the energy content of the atoms or molecules.
When ultraviolet radiations are absorbed, this results in the excitation of the electrons from the ground state towards a higher energy state.
Molecules containing π-electrons or nonbonding electrons (n-electrons) can absorb energy in the form of ultraviolet light to excite these electrons to higher anti-bonding molecular orbitals.
The more easily excited the electrons, the longer the wavelength of light they can absorb. There are four possible types of transitions (π–π*, n–π*, σ–σ*, and n–σ*), and they can be ordered as follows: σ–σ* > n–σ* > π–π* > n–π* The absorption of ultraviolet light by a chemical compound will produce a distinct spectrum that aids in the identification of the compound.
This document summarizes key concepts from a chapter on atomic structure:
1. Electromagnetic radiation consists of oscillating electric and magnetic fields that propagate as waves. Light is a type of electromagnetic radiation detectable by the human eye.
2. Atoms can only absorb or emit electromagnetic radiation at specific quantized energy levels. This explains the emission spectrum of hydrogen, which shows only certain discrete wavelengths.
3. Niels Bohr's early model of the hydrogen atom proposed that electrons orbit the nucleus at fixed distances corresponding to discrete energy levels. Later, the quantum mechanical model described electron behavior as wave-like standing waves.
4. Werner Heisenberg's uncertainty principle states that the more precisely the position
UV-visible spectroscopy is a technique that uses light in the visible and adjacent ranges. It works by measuring how much light is absorbed by a sample at each wavelength.
The document discusses the basic principles of spectroscopy, including how electromagnetic radiation interacts with matter. It describes the laws of absorption, specifically Beer's law, which states that absorbance is proportional to concentration.
The key aspects of instrumentation are outlined, including light sources, wavelength selectors like monochromators, sample holders, and detection devices. Single beam and double beam spectrophotometers are explained as the main types of instruments used in UV-visible spectroscopy.
The document summarizes a presentation given by Sulabh Pal, Suresh Kumar, and Himanshu Srivastava on April 27th 2012 about an ant colony optimization technique proposed for edge detection in images. The presentation covered the historical background of ant colony optimization, described how it works by modeling the behavior of ant colonies, and presented experimental results showing that the proposed approach improves edge detection compared to traditional methods and has shorter computation time than traditional ant colony optimization. The technique was also discussed as having applications in optimization problems like routing in communication networks.
- The document is a presentation on ultraviolet spectroscopy submitted by Moriyom Akhter and Md Shah Alam from the Department of Pharmacy at World University of Bangladesh.
- It defines ultraviolet spectroscopy and discusses key concepts like absorption spectra, types of electronic transitions that can occur, Beer's and Lambert's absorption laws, instrumentation components, and applications in qualitative and quantitative analysis.
- The presentation also examines effects of chromophores and auxochromes on absorption spectra and maximum wavelengths, and how solvents can shift absorption peaks.
Spectroscopy involves the interaction of electromagnetic radiation with matter. Spectroscopic methods are used to elucidate molecular structure and quantify inorganic and organic compounds. There are several regions of the electromagnetic spectrum used including X-ray, UV, visible, and IR. Important concepts include Beer's law, which states absorbance is proportional to concentration, molar absorptivity, and path length. Spectrophotometry is used for qualitative and quantitative analysis in areas such as determining unknown concentrations. Fluorescence also provides a sensitive technique where molecules emit light at longer wavelengths after absorbing radiation.
This document discusses the Beer-Lambert law, which states that the absorbance of light as it passes through a substance is directly proportional to the concentration of that substance and the path length. It provides the mathematical expression of the Beer-Lambert law and defines terms such as transmittance and absorbance. The document explains that absorbance is preferred over transmittance for expressing the Beer-Lambert law because absorbance results in a linear relationship with concentration that allows for simple quantitative analysis. Several examples are provided to demonstrate applications of the Beer-Lambert law.
This document provides an introduction to spectrometric methods and the Beer-Lambert law. It defines key terms like absorbance, transmittance, molar absorptivity, and wavelength. The Beer-Lambert law states that absorbance is directly proportional to concentration, path length, and molar absorptivity. It also explains that absorbance follows a linear relationship with concentration at a given path length and wavelength for a single analyte. Deviations from Beer's law can occur under certain circumstances.
This document provides an overview of UV-Visible spectroscopy. It discusses how UV radiation causes electronic transitions in molecules, which can be observed via absorption spectroscopy. The instrumentation used includes sources of UV and visible light, a monochromator to select wavelengths, and a detector. Samples are dissolved and placed in transparent cuvettes for analysis. Spectra are recorded as absorbances and show absorption bands corresponding to electronic transitions. UV-Vis is useful for structure elucidation and quantitative analysis.
UV-Visible spectroscopy involves absorption of ultraviolet or visible light by molecules. This absorption causes electrons to move to higher energy molecular orbitals. The Beer-Lambert law states that absorbance is directly proportional to concentration and path length. Deviations from Beer-Lambert law can occur at high concentrations due to interactions between molecules, or if non-monochromatic light is used. UV-Visible spectroscopy is used to study electronic transitions and structure of molecules.
Solving Quadratic Assignment Problems (QAP) using Ant Colony SystemAjay Bidyarthy
The document describes using an ant colony system algorithm to solve quadratic assignment problems (QAP). QAPs have applications in operations research, parallel computing, and combinatorial data analysis. The ant colony system is applied to QAP by modeling it as assigning activities to locations. Ants probabilistically construct solutions based on pheromone trails and distance/flow matrices. The algorithm runs in O(mn2k) time which is faster than exact solutions for large problems. Example problems and results demonstrating the ant colony system finding near-optimal solutions to standard QAP test cases are presented.
UV spectroscopy can be used to analyze organic compounds. It works by measuring the absorption of UV or visible light. Double beam UV spectroscopy has advantages over single beam as it automatically corrects for fluctuations in light source intensity and detector response. UV spectroscopy can be used to detect impurities, characterize functional groups, and determine concentrations through the Beer-Lambert law. It provides structural information about organic compounds.
UV-VIS spectroscopy involves using ultraviolet or visible light to illuminate a sample and analyzing the light that is absorbed. Electronic transitions in molecules can be detected by observing which wavelengths of light are absorbed. This provides information about functional groups and conjugated systems present in the sample. A UV-VIS spectrophotometer directs light from a source through the sample solution and a monochromator selects wavelengths, which are then measured by a detector. The amount of light absorbed at each wavelength follows Beer's Law, allowing for determination of concentrations from a calibration curve.
The document discusses the derivation of Beer-Lambert's law, which relates the absorption of light to the properties of the material through which the light is passing. Lambert first derived a relationship showing that the decrease in light intensity through a medium is directly proportional to the intensity and thickness of the medium. Beer later extended this by showing absorption also depends on the concentration of the absorbing solution. Together, Beer and Lambert derived an equation, now known as Beer-Lambert's law, that quantifies the relationship between light absorption and intensity, thickness of the medium, and concentration of an absorbing solution. The law has limitations in that it applies only to monochromatic, unscattered light passing through dilute solutions.
The document discusses UV-Vis spectroscopy, including an introduction to electronic transitions observed in UV-Vis spectroscopy, instrumentation used in UV-Vis spectroscopy, and components of UV-Vis spectrometers such as sources, sample containers, monochromators, and detectors. Selection rules that determine which electronic transitions are allowed are also covered.
UV-Vis spectroscopy involves using spectroscopy to study the interaction between electromagnetic radiation and matter. It summarizes that UV-Vis spectroscopy uses electromagnetic waves in the UV and visible spectral regions to analyze molecules and their electronic transitions. The document discusses the wave and particle theories of light, the electromagnetic spectrum, Beer-Lambert law which relates absorbance to concentration, and limitations of the Beer-Lambert law such as deviations at high/low concentrations and due to fluorescence or turbidity.
Bat Algorithm is Better Than Intermittent Search StrategyXin-She Yang
This document compares the bat algorithm to the intermittent search strategy for balancing exploration and exploitation in metaheuristic optimization algorithms. It reviews several metaheuristic algorithms and analyzes the theoretical basis for optimal balancing of exploration and exploitation phases. Equations are presented for the optimal ratio of exploration and exploitation phases in 2D problems based on the intermittent search strategy. The bat algorithm is described and its ability to achieve near-optimal balancing is demonstrated through numerical experiments on test functions. The document concludes higher dimensional problems require more exploration effort to find global optima with limited computations.
This document summarizes a research paper that proposes a new swarm intelligence algorithm called a Hybrid Bat Algorithm. The Hybrid Bat Algorithm combines the original Bat Algorithm with strategies from Differential Evolution. The Bat Algorithm is based on the echolocation behavior of bats and has been shown to effectively solve lower-dimensional optimization problems. However, it can struggle with higher-dimensional problems due to its tendency to converge quickly. The researchers propose hybridizing it with Differential Evolution strategies to improve its performance on higher-dimensional problems. They test the Hybrid Bat Algorithm on standard benchmark functions and find that it significantly outperforms the original Bat Algorithm.
A New Metaheuristic Bat-Inspired AlgorithmXin-She Yang
This document proposes a new metaheuristic optimization algorithm called the Bat Algorithm (BA) which is inspired by the echolocation behavior of microbats. Microbats use echolocation to detect prey and navigate in darkness by emitting ultrasonic pulses and analyzing the echo. The BA idealizes these behaviors to develop rules for how "bats" can search for the optimal solution. Key behaviors include adjusting pulse rates and loudness based on proximity to the target solution. The BA shows potential to combine advantages of other algorithms like PSO and is shown to perform well in simulations.
The document summarizes a seminar presentation on the bat optimization algorithm. It introduces the algorithm which is based on echolocation behavior of microbats. It describes how bats emit sound pulses to locate prey and adjust parameters like frequency, wavelength, and loudness. The pseudo code and flowchart of the bat algorithm are provided. Variations of the algorithm including multi-objective and fuzzy logic versions are mentioned. Applications to engineering design, scheduling, and data mining are listed. Advantages include simplicity and quick convergence, while disadvantages include potential for stagnation.
محاضرات متقدمة تدرس لطلاب حاسبات بنى سويف السنة الثالثة لتنمية قدراتهم البحثية وهذة الموضوعات تدرس على مستوى الدكتوراة - - نريد تميز طلاب حاسبات ليتميزو فى البحث العلمى -
This document provides an overview of swarm robotics. It begins with examples of decentralized control and self-organization in natural swarms like ants and bees. It then discusses how swarm robotics takes inspiration from these systems, using local control methods, local communication, and self-organization to complete collective tasks without centralized control. The rest of the document focuses on a proposed system for gesture recognition to allow human control of swarm robots. It describes hand detection, feature extraction, and hardware implementation using three foot-bot robots. It concludes with potential applications of swarm robotics and areas for future work.
Swarm intelligence refers to the collective behavior that emerges from decentralized, self-organized systems, both natural and artificial. In nature, it can be seen in the ability of ant colonies and bird flocks to coordinate and complete tasks through simple local interactions between individuals. Artificial swarm intelligence systems are distributed systems of interacting autonomous agents that coordinate through self-organization to solve problems through cooperation and division of labor. Examples of algorithms inspired by swarm intelligence include ant colony optimization and particle swarm optimization.
This document discusses particle swarm optimization (PSO), which is an optimization technique inspired by swarm intelligence and the social behavior of bird flocking or fish schooling. PSO uses a population of candidate solutions called particles that fly through the problem hyperspace, with each particle adjusting its position based on its own experience and the experience of neighboring particles. The algorithm iteratively improves the particles' positions to locate the best solution based on fitness evaluations.
The document discusses particle swarm optimization (PSO), a population-based stochastic optimization technique inspired by bird flocking and fish schooling behavior. PSO initializes a population of random particles in search space and updates their positions and velocities based on their own experience and neighboring particles' experience to move toward optimal solutions. Compared to genetic algorithms, PSO does not use genetic operators and particles have memory of their own best solution to guide the search. The document also provides an overview of ant colony optimization, another swarm intelligence technique modeled after ant colony behavior.
Bat Algorithm: A Novel Approach for Global Engineering OptimizationXin-She Yang
The document summarizes a novel bat algorithm approach for engineering optimization problems. The algorithm is inspired by the echolocation behavior of microbats. Microbats use echolocation to detect prey and navigate in the dark by emitting ultrasonic sound pulses and analyzing the echo. The bat algorithm idealizes this behavior by associating the echo with the objective function to be optimized. Preliminary studies show the bat algorithm is promising for solving complex engineering optimization problems.
Bat Algorithm: A Novel Approach for Global Engineering OptimizationXin-She Yang
The document introduces a new metaheuristic optimization algorithm called the Bat Algorithm (BA) which is inspired by the echolocation behavior of microbats. The BA is formulated based on echolocation characteristics such as loudness variation and pulse emission rates. The BA is tested on eight well-known nonlinear engineering optimization problems and is found to perform better than existing algorithms. The unique search features of the BA are analyzed and its potential for future research is discussed.
Bat Algorithm for Multi-objective OptimisationXin-She Yang
This document proposes a multi-objective bat algorithm (MOBA) to solve multi-objective optimization problems. MOBA extends the previously developed bat algorithm for single objective optimization problems. MOBA uses Pareto dominance to evaluate non-dominated solutions and find an approximation of the true Pareto front. It initializes a population of bats and updates their positions and velocities over iterations to explore the search space. The best current solutions are used to guide the bats towards non-dominated regions.
The document summarizes the bat algorithm, a metaheuristic optimization algorithm inspired by bat echolocation behavior. Bats emit sounds and use echoes to locate prey and obstacles. The bat algorithm idealizes these characteristics, with bats represented as solution vectors flying with velocities, frequencies, and loudness adjusted based on proximity to prey. The algorithm is extended to multi-objective optimization problems by combining objective functions into a single objective using weights and finding non-dominated solutions.
Firefly Algorithms for Multimodal OptimizationXin-She Yang
This document summarizes a research paper on using a new Firefly Algorithm (FA) for multimodal optimization problems. The FA is inspired by the flashing behavior of fireflies. It is described as being superior to other metaheuristic algorithms like Particle Swarm Optimization (PSO) based on simulations. The FA works by having fireflies that represent solution points move towards more attractive (brighter) fireflies within their visible range, with attractiveness decreasing with distance.
- The document describes testing a maximum entropy method (MaxEnt) for extracting gravitational wave signals from noisy detector data.
- Ringdown waveforms were injected into artificially constructed noise matching LIGO detector sensitivity. MaxEnt then extracted the signals blindly.
- The extracted signals' parameters, such as frequency and decay constant, were estimated and compared to the original injected parameters to evaluate MaxEnt's effectiveness.
- Results showed MaxEnt could extract parameters accurately at high signal-to-noise ratios but extracted noisier signals at lower ratios, as expected.
Firefly Algorithm, Levy Flights and Global OptimizationXin-She Yang
The document describes a new metaheuristic optimization algorithm called the L ́evy-flight Firefly Algorithm (LFA) that combines L ́evy flights with the search strategy of the Firefly Algorithm. The LFA is formulated by incorporating the characteristics of L ́evy flights into the idealized rules of the Firefly Algorithm. Numerical studies show that the LFA converges more quickly than existing algorithms like Particle Swarm Optimization and finds global optima more naturally. The LFA is compared to PSO and genetic algorithms on standard test functions, and results show the LFA reaches global optima in fewer evaluations on average.
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A New Metaheuristic Bat-Inspired Algorithm
1. arXiv:1004.4170v1[math.OC]23Apr2010
A New Metaheuristic Bat-Inspired Algorithm
Xin-She Yang
Department of Engineering, University of Cambridge,
Trumpington Street, Cambridge CB2 1PZ, UK
Abstract
Metaheuristic algorithms such as particle swarm optimization, firefly algorithm and
harmony search are now becoming powerful methods for solving many tough optimiza-
tion problems. In this paper, we propose a new metaheuristic method, the Bat Algo-
rithm, based on the echolocation behaviour of bats. We also intend to combine the
advantages of existing algorithms into the new bat algorithm. After a detailed formu-
lation and explanation of its implementation, we will then compare the proposed algo-
rithm with other existing algorithms, including genetic algorithms and particle swarm
optimization. Simulations show that the proposed algorithm seems much superior to
other algorithms, and further studies are also discussed.
Citation detail:
X.-S. Yang, A New Metaheuristic Bat-Inspired Algorithm, in: Nature Inspired Coop-
erative Strategies for Optimization (NISCO 2010) (Eds. J. R. Gonzalez et al.), Studies
in Computational Intelligence, Springer Berlin, 284, Springer, 65-74 (2010).
1 Introduction
Metaheuristic algorithms such as particle swarm optimization and simulated annealing
are now becoming powerful methods for solving many tough optimization problems [3-
7,11]. The vast majority of heuristic and metaheuristic algorithms have been derived
from the behaviour of biological systems and/or physical systems in nature. For exam-
ple, particle swarm optimization was developed based on the swarm behaviour of birds
and fish [7, 8], while simulated annealing was based on the annealing process of metals
[9].
New algorithms are also emerging recently, including harmony search and the firefly
algorithm. The former was inspired by the improvising process of composing a piece
of music [4], while the latter was formulated based on the flashing behaviour of fireflies
[14]. Each of these algorithms has certain advantages and disadvantages. For example,
simulating annealing can almost guarantee to find the optimal solution if the cooling
process is slow enough and the simulation is running long enough; however, the fine
adjustment in parameters does affect the convergence rate of the optimization process.
A natural question is whether it is possible to combine major advantages of these
algorithms and try to develop a potentially better algorithm? This paper is such an
attempt to address this issue.
1
2. In this paper, we intend to propose a new metaheuristic method, namely, the Bat
Algorithm (BA), based on the echolocation behaviour of bats. The capability of echolo-
cation of microbats is fascinating as these bats can find their prey and discriminate
different types of insects even in complete darkness. We will first formulate the bat
algorithm by idealizing the echolocation behaviour of bats. We then describe how it
works and make comparison with other existing algorithms. Finally, we will discuss
some implications for further studies.
2 Echolocation of bats
2.1 Behaviour of microbats
Bats are fascinating animals. They are the only mammals with wings and they also have
advanced capability of echolocation. It is estimated that there are about 996 different
species which account for up to 20% of all mammal species [1, 2]. Their size ranges from
the tiny bumblebee bat (of about 1.5 to 2g) to the giant bats with wingspan of about 2
m and weight up to about 1 kg. Microbats typically have forearm length of about 2.2 to
11cm. Most bats uses echolocation to a certain degree; among all the species, microbats
are a famous example as microbats use echolocation extensively while megabats do not
[12, 13].
Most microbats are insectivores. Microbats use a type of sonar, called, echolocation,
to detect prey, avoid obstacles, and locate their roosting crevices in the dark. These bats
emit a very loud sound pulse and listen for the echo that bounces back from the sur-
rounding objects. Their pulses vary in properties and can be correlated with their hunt-
ing strategies, depending on the species. Most bats use short, frequency-modulated sig-
nals to sweep through about an octave, while others more often use constant-frequency
signals for echolocation. Their signal bandwidth varies depends on the species, and
often increased by using more harmonics.
2.2 Acoustics of Echolocation
Though each pulse only lasts a few thousandths of a second (up to about 8 to 10 ms),
however, it has a constant frequency which is usually in the region of 25kHz to 150
kHz. The typical range of frequencies for most bat species are in the region between
25kHz and 100kHz, though some species can emit higher frequencies up to 150 kHz.
Each ultrasonic burst may last typically 5 to 20 ms, and microbats emit about 10 to 20
such sound bursts every second. When hunting for prey, the rate of pulse emission can
be sped up to about 200 pulses per second when they fly near their prey. Such short
sound bursts imply the fantastic ability of the signal processing power of bats. In fact,
studies shows the integration time of the bat ear is typically about 300 to 400 µs.
As the speed of sound in air is typically v = 340 m/s, the wavelength λ of the
ultrasonic sound bursts with a constant frequency f is given by
λ =
v
f
, (1)
which is in the range of 2mm to 14mm for the typical frequency range from 25kHz to
150 kHz. Such wavelengths are in the same order of their prey sizes.
2
3. Amazingly, the emitted pulse could be as loud as 110 dB, and, fortunately, they
are in the ultrasonic region. The loudness also varies from the loudest when searching
for prey and to a quieter base when homing towards the prey. The travelling range of
such short pulses are typically a few metres, depending on the actual frequencies [12].
Microbats can manage to avoid obstacles as small as thin human hairs.
Studies show that microbats use the time delay from the emission and detection of
the echo, the time difference between their two ears, and the loudness variations of the
echoes to build up three dimensional scenario of the surrounding. They can detect the
distance and orientation of the target, the type of prey, and even the moving speed of
the prey such as small insects. Indeed, studies suggested that bats seem to be able to
discriminate targets by the variations of the Doppler effect induced by the wing-flutter
rates of the target insects [1].
Obviously, some bats have good eyesight, and most bats also have very sensitive
smell sense. In reality, they will use all the senses as a combination to maximize the
efficient detection of prey and smooth navigation. However, here we are only interested
in the echolocation and the associated behaviour.
Such echolocation behaviour of microbats can be formulated in such a way that it
can be associated with the objective function to be optimized, and this make it possible
to formulate new optimization algorithms. In the rest of this paper, we will first outline
the basic formulation of the Bat Algorithm (BA) and then discuss the implementation
and comparison in detail.
3 Bat Algorithm
If we idealize some of the echolocation characteristics of microbats, we can develop var-
ious bat-inspired algorithms or bat algorithms. For simplicity, we now use the following
approximate or idealized rules:
1. All bats use echolocation to sense distance, and they also ‘know’ the difference
between food/prey and background barriers in some magical way;
2. Bats fly randomly with velocity vi at position xi with a fixed frequency fmin,
varying wavelength λ and loudness A0 to search for prey. They can automatically
adjust the wavelength (or frequency) of their emitted pulses and adjust the rate
of pulse emission r ∈ [0, 1], depending on the proximity of their target;
3. Although the loudness can vary in many ways, we assume that the loudness varies
from a large (positive) A0 to a minimum constant value Amin.
Another obvious simplification is that no ray tracing is used in estimating the time
delay and three dimensional topography. Though this might be a good feature for
the application in computational geometry, however, we will not use this as it is more
computationally extensive in multidimensional cases.
In addition to these simplified assumptions, we also use the following approxima-
tions, for simplicity. In general the frequency f in a range [fmin, fmax] corresponds to
a range of wavelengths [λmin, λmax]. For example a frequency range of [20kHz, 500kHz]
corresponds to a range of wavelengths from 0.7mm to 17mm.
For a given problem, we can also use any wavelength for the ease of implementation.
In the actual implementation, we can adjust the range by adjusting the wavelengths
(or frequencies), and the detectable range (or the largest wavelength) should be chosen
3
4. Bat Algorithm
Objective function f(x), x = (x1, ..., xd)T
Initialize the bat population xi (i = 1, 2, ..., n) and vi
Define pulse frequency fi at xi
Initialize pulse rates ri and the loudness Ai
while (t <Max number of iterations)
Generate new solutions by adjusting frequency,
and updating velocities and locations/solutions [equations (2) to (4)]
if (rand > ri)
Select a solution among the best solutions
Generate a local solution around the selected best solution
end if
Generate a new solution by flying randomly
if (rand < Ai & f(xi) < f(x∗))
Accept the new solutions
Increase ri and reduce Ai
end if
Rank the bats and find the current best x∗
end while
Postprocess results and visualization
Figure 1: Pseudo code of the bat algorithm (BA).
such that it is comparable to the size of the domain of interest, and then toning down
to smaller ranges. Furthermore, we do not necessarily have to use the wavelengths
themselves, instead, we can also vary the frequency while fixing the wavelength λ. This
is because λ and f are related due to the fact λf is constant. We will use this later
approach in our implementation.
For simplicity, we can assume f ∈ [0, fmax]. We know that higher frequencies have
short wavelengths and travel a shorter distance. For bats, the typical ranges are a few
metres. The rate of pulse can simply be in the range of [0, 1] where 0 means no pulses
at all, and 1 means the maximum rate of pulse emission.
Based on these approximations and idealization, the basic steps of the Bat Algorithm
(BA) can be summarized as the pseudo code shown in Fig. 1.
3.1 Movement of Virtual Bats
In simulations, we use virtual bats naturally. We have to define the rules how their
positions xi and velocities vi in a d-dimensional search space are updated. The new
solutions xt
i and velocities vt
i at time step t are given by
fi = fmin + (fmax − fmin)β, (2)
vt
i = vt−1
i + (xt
i − x∗)fi, (3)
xt
i = xt−1
i + vt
i, (4)
where β ∈ [0, 1] is a random vector drawn from a uniform distribution. Here x∗ is the
current global best location (solution) which is located after comparing all the solutions
4
5. among all the n bats. As the product λifi is the velocity increment, we can use either fi
(or λi ) to adjust the velocity change while fixing the other factor λi (or fi), depending
on the type of the problem of interest. In our implementation, we will use fmin = 0 and
fmax = 100, depending the domain size of the problem of interest. Initially, each bat is
randomly assigned a frequency which is drawn uniformly from [fmin, fmax].
For the local search part, once a solution is selected among the current best solutions,
a new solution for each bat is generated locally using random walk
xnew = xold + ǫAt
, (5)
where ǫ ∈ [−1, 1] is a random number, while At
=<At
i > is the average loudness of all
the bats at this time step.
The update of the velocities and positions of bats have some similarity to the pro-
cedure in the standard particle swarm optimization [7] as fi essentially controls the
pace and range of the movement of the swarming particles. To a degree, BA can be
considered as a balanced combination of the standard particle swarm optimization and
the intensive local search controlled by the loudness and pulse rate.
3.2 Loudness and Pulse Emission
Furthermore, the loudness Ai and the rate ri of pulse emission have to be updated
accordingly as the iterations proceed. As the loudness usually decreases once a bat has
found its prey, while the rate of pulse emission increases, the loudness can be chosen
as any value of convenience. For example, we can use A0 = 100 and Amin = 1. For
simplicity, we can also use A0 = 1 and Amin = 0, assuming Amin = 0 means that a bat
has just found the prey and temporarily stop emitting any sound. Now we have
At+1
i = αAt
i, rt+1
i = r0
i [1 − exp(−γt)], (6)
where α and γ are constants. In fact, α is similar to the cooling factor of a cooling
schedule in the simulated annealing [9]. For any 0 < α < 1 and γ > 0, we have
At
i → 0, rt
i → r0
i , as t → ∞. (7)
In the simplicity case, we can use α = γ, and we have used α = γ = 0.9 in our
simulations. The choice of parameters requires some experimenting. Initially, each
bat should have different values of loudness and pulse emission rate, and this can be
achieved by randomization. For example, the initial loudness A0
i can typically be [1, 2],
while the initial emission rate r0
i can be around zero, or any value r0
i ∈ [0, 1] if using
(6). Their loudness and emission rates will be updated only if the new solutions are
improved, which means that these bats are moving towards the optimal solution.
4 Validation and Comparison
From the pseudo code, it is relatively straightforward to implement the Bat Algorithm
in any programming language. For the ease of visualization, we have implemented it
using Matlab for various test functions.
5
6. −5 0 5
−5
0
5
Figure 2: The paths of 25 virtual bats during 20 consecutive iterations. They converge into
(1, 1).
4.1 Benchmark Functions
There are many standard test functions for validating new algorithms. In the current
benchmark validation, we have chosen the well-known Rosenbrock’s function
f(x) =
d−1
i=1
(1 − x2
i )2
+ 100(xi+1 − x2
i )2
, −2.048 ≤ xi ≤ 2.048, (8)
and the eggcrate function
g(x, y) = x2
+ y2
+ 25(sin2
x + sin2
y), (x, y) ∈ [−2π, 2π] × [−2π, 2π]. (9)
We know that f(x) has a global minimum fmin = 0 at (1, 1) in 2D, while g(x, y) has a
global minimum gmin = 0 at (0, 0). De Jong’s standard sphere function
h(x) =
d
i=1
x2
i , −10 ≤ xi ≤ 10, (10)
has also been used. Its minimum is hmin = 0 at (0, 0, ..., 0) for any d ≥ 3.
In addition, we have also used other standard test functions for numerical global
optimization [10] such as Ackley’s function
s(x) = 20 + e − 20 exp − 0.2
1
d
d
i=1
x2
i − exp[
1
d
d
i=1
cos(2πxi)], (11)
6
7. −5
0
5
−5
0
5
0
20
40
60
80
100
−5 0 5
−5
−4
−3
−2
−1
0
1
2
3
4
5
Figure 3: The eggcrate function (left) and the locations of 40 bats in the last ten iterations
(right).
where −30 ≤ xi ≤ 30. It has the global minimum smin = 0 at (0, 0, ..., 0).
Michalewicz’s test function
f(x) = −
d
i=1
sin(xi) sin(
ix2
i
π
)
2m
, (m = 10), (12)
has d! local optima in the the domain 0 ≤ xi ≤ π where i = 1, 2, ..., d. The global
minimum is f∗ ≈ −1.801 for d = 2, while f∗ ≈ −4.6877 for d = 5.
In our implementation, we use n = 25 to 50 virtual bats, and α = 0.9. For Rosen-
brock’s 2-D banana function, the paths of 25 virtual bats during the consecutive 20 time
steps are shown in Fig. 2 where we can see that the bats converge at the global opti-
mum (1, 1). For the multimodal eggcrate function, a snapshot of the last 10 iterations
is shown in Fig. 3. Again, all bats move towards the global best (0, 0).
4.2 Comparison with Other Algorithms
In order to compare the performance of the new algorithm, we have tested it against
other heuristic algorithms, including genetic algorithms (GA) [5, 6, 11], and particle
swarm optimization (PSO) [7, 8]. There are many variants of PSO, and some variants
such as the mean PSO could perform better than the standard PSO [3]; however, the
standard PSO is by far the most popularly used. Therefore, we will also use the standard
PSO in our comparison.
There are many ways to carry out the comparison of algorithm performance, and
two obvious approaches are: to compare the numbers of function evaluations for a
given tolerance or accuracy, or to compare their accuracies for a fixed number of func-
tion evaluations. Here we will use the first approach. In our simulations, we use a
fixed tolerance ǫ ≤ 10−5
, and we run each algorithm for 100 times so that we can do
meaningful statistical analysis.
7
8. For genetic algorithms, we have used the standard version with no elitism with
the mutation probability of pm = 0.05 and crossover probability of 0.95. For particle
swarm optimization, we have also used the standard version with learning parameters
α = =
¯
2 and the inertia function I = 1 [7, 8]. The simulations have been carried out
using Matlab on a standard 3GHz desktop computer. Each run with about 10,000
function evaluations typically takes less than 5 seconds. Furthermore, we have tried to
use different population sizes from n = 10 to 250, and we found that for most problems,
n = 15 to 50 is sufficient. Therefore, we use a fixed population n = 40 for all simulations.
Table 1 shows the number of function evaluations in the form of mean ± the standard
deviation (success rate of the algorithm in finding the global optima).
Table 1: Comparison of BA with GA, and PSO.
Functions/Algorithms GA PSO BA
Multiple peaks 52124 ± 3277(98%) 3719 ± 205(97%) 1152 ± 245(100%)
Michalewicz’s (d=16) 89325 ± 7914(95%) 6922 ± 537(98%) 4752 ± 753(100%)
Rosenbrock’s (d=16) 55723 ± 8901(90%) 32756 ± 5325(98%) 7923 ± 3293(100%)
De Jong’s (d=256) 25412 ± 1237(100%) 17040 ± 1123(100%) 5273 ± 490(100%)
Schwefel’s (d=128) 227329 ± 7572(95%) 14522 ± 1275(97%) 8929 ± 729(99%)
Ackley’s (d=128) 32720 ± 3327(90%) 23407 ± 4325(92%) 6933 ± 2317(100%)
Rastrigin’s 110523 ± 5199(77%) 79491 ± 3715(90%) 12573 ± 3372(100%)
Easom’s 19239 ± 3307(92%) 17273 ± 2929(90%) 7532 ± 1702(99%)
Griewangk’s 70925 ± 7652(90%) 55970 ± 4223(92%) 9792 ± 4732(100%)
Shubert’s (18 minima) 54077 ± 4997(89%) 23992 ± 3755(92%) 11925 ± 4049(100%)
From Table 1, we can see that PSO performs much better than genetic algorithms,
while the Bat Algorithm is much superior to other algorithms in terms of accuracy and
efficiency. This is no surprising as the aim of developing the new algorithm was to try
to use the advantages of existing algorithms and other interesting feature inspired by
the fantastic behaviour of echolocation of microbats.
If we replace the variations of the frequency fi by a random parameter and setting
Ai = 0 and ri = 1, the bat algorithm essentially becomes the standard Particle Swarm
Optimization (PSO). Similarly, if we do not use the velocities, but we use fixed loudness
and rate: Ai and ri. For example, Ai = ri = 0.7, this algorithm is virtually reduced to
a simple Harmony Search (HS) as the frequency/wavelength change is essentially the
pitch adjustment, while the rate of pulse emission is similar to the harmonic acceptance
rate (here with a twist) in the harmony search algorithm [4, 15]. The current studies
implies that the proposed new algorithm is potentially more powerful and thus should
be investigated further in many applications of engineering and industrial optimization
problems.
5 Discussions
In this paper, we have successfully formulated a new Bat Algorithm for continuous
constrained optimization problems. From the formulation of the Bat Algorithm and its
implementation and comparison, we can see that it is a very promising algorithm. It is
8
9. potentially more powerful than particle swarm optimization and genetic algorithms as
well as Harmony Search. The primary reason is that BA uses a good combination of
major advantages of these algorithms in some way. Moreover, PSO and harmony search
are the special cases of the Bat Algorithm under appropriate simplifications.
In addition, the fine adjustment of the parameters α and γ can affect the convergence
rate of the bat algorithm. In fact, parameter α acts in a similar role as the cooling
schedule in the simulated annealing. Though the implementation is more complicated
than many other metaheuristic algorithms; however, it does show that it utilizes a
balanced combination of the advantages of existing successful algorithms with innovative
feature based on the echolocation behaviour of bats. New solutions are generated by
adjusting frequencies, loudness and pulse emission rates, while the proposed solution is
accepted or not depends on the quality of the solutions controlled or characterized by
loudness and pulse rate which are in turn related to the closeness or the fitness of the
locations/solution to the global optimal solution.
The exciting results suggest that more studies will highly be needed to carry out
the sensitivity analysis, to analyze the rate of algorithm convergence, and to improve
the convergence rate even further. More extensive comparison studies with a more
wide range of existing algorithms using much tough test functions in higher dimensions
will pose more challenges to the algorithms, and thus such comparisons will potentially
reveal the virtues and weakness of all the algorithms of interest.
An interesting extension will be to use different schemes of wavelength or frequency
variations instead of the current linear implementation. In addition, the rates of pulse
emission and loudness can also be varied in a more sophisticated manner. Another
extension for discrete problems is to use the time delay between pulse emission and
the echo bounced back. For example, in the travelling salesman problem, the distance
between two adjacent nodes/cities can easily be coded as time delay. As microbats use
time difference between their two ears to obtain three-dimensional information, they can
identify the type of prey and the velocity of a flying insect. Therefore, a further natural
extension to the current bat algorithm would be to use the directional echolocation and
Doppler effect, which may lead to even more interesting variants and new algorithms.
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